This invention pertains to microlithography apparatus and methods for use, e.g., in the manufacture of semiconductor integrated circuits, displays, and the like. The subject apparatus and methods utilize a charged particle beam (e.g., electron beam or ion beam) as an energy beam for transferring a pattern, defined by a reticle or mask, onto a sensitive substrate (e.g., semiconductor wafer or the like). More specifically, the invention is directed to such apparatus and methods exhibiting reduced deflection aberrations even while effecting large beam deflections.
Conventional exposure formats in charged-particle-beam (CPB) microlithography apparatus can be categorized into the following three types:
(1) Spot-beam exposure
(2) Variable shaped beam exposure
(3) Block exposure
Although these exposure formats exhibit superior resolution compared with conventional batch-transfer systems employing visible light as an energy beam, they exhibit disappointingly low xe2x80x9cthroughputxe2x80x9d (number of substrates or wafers that can be processed per unit time). Throughput is especially low with exposure formats (1) and (2) because the patterns are exposed by being traced with a beam having an extremely small spot radius or having an extremely small square transverse profile.
The block exposure format (3) was developed to improve throughput. In block exposure, uniformly shaped features are defined on a reticle, and portions of the reticle containing such features are exposed one shot at a time in batches. Because the number of features that can be placed on a reticle is limited in this format, a variable-profile exposure system must be used. Consequently, throughput is not improved as much as would otherwise be expected.
In order to further improve throughput, so-called xe2x80x9cdividedxe2x80x9d projection-transfer apparatus have been developed. In such apparatus, the reticle defining a pattern is divided into multiple portions or xe2x80x9cexposure unitsxe2x80x9d that are individually projection-exposed onto the substrate. Each exposure unit requires a respective xe2x80x9cshotxe2x80x9d (exposure) using the energy beam.
Certain aspects of a conventional divided projection-transfer apparatus are depicted in FIGS. 13 and 14. Referring first to FIG. 13, an entire substrate (wafer) W is shown containing multiple xe2x80x9cchipsxe2x80x9d C. Each chip C contains multiple xe2x80x9cstripesxe2x80x9d S, and each stripe S contains multiple xe2x80x9csubfieldsxe2x80x9d SF (as representative exposure units). The reticle (not shown) defining the pattern for each chip C is similarly divided into multiple stripes and subfields.
Each subfield SF is individually exposed. Exposure is normally performed in a manner as shown in FIG. 14, in which the reticle is situated upstream of the substrate. As a charged particle beam (e.g., electron beam) illuminates each subfield on the reticle, the respective portion of the pattern is projected by a projection-optical system (not shown but understood to be located between the reticle and the substrate) onto the substrate, thereby imprinting the pattern portion onto a respective region of the substrate. The subfields in each stripe are arranged in columns. The columns are sequentially exposed, and the subfields in each column are sequentially exposed. To effect serial exposure of the columns, the reticle and substrate (which are mounted on respective stages that are not shown) undergo relative linear motions in respective scan directions at respective constant scan velocities. The respective scan velocities of the reticle stage and wafer stage are established by, inter alia, the demagnification ratio of the projection-optical system.
Before reaching the reticle, the charged particle beam (generated by a suitable source) passes as an xe2x80x9cillumination beamxe2x80x9d through an xe2x80x9cillumination-optical systemxe2x80x9d located upstream of the reticle. To expose the subfields in each column of a stripe on the reticle, the illumination beam is deflected (by appropriately situated deflectors in the illumination-optical system) in a direction roughly perpendicular to the direction of linear motion of the reticle stage. Thus, the subfields in each stripe are sequentially exposed by the illumination beam in a raster manner. After passing through the reticle, the beam (now termed the xe2x80x9cpatterned beamxe2x80x9d) passes through a xe2x80x9cprojection-optical systemxe2x80x9d to the substrate. The illumination-optical system and projection-optical system are collectively termed the xe2x80x9cCPB optical system.xe2x80x9d As each column of subfields is exposed, the reticle and substrate are moved in opposite directions to position the next column of subfields in the stripe for exposure. To improve throughput, each subsequent column of subfields is exposed by deflecting the charged particle beam in a direction opposite the direction in which the beam was deflected in the previous column, as shown in FIG. 14.
The subfields on the reticle are separated from one another by struts. The struts strengthen and add rigidity to the reticle, and also facilitate the illumination of only one subfield per shot.
To improve throughput, the illumination beam usually has a relatively high beam current. However, high beam currents tend to introduce significant image blur due to Coulomb effects. A conventional approach for reducing such Coulomb effects is to enlarge the area being exposed per shot and to subject the illumination beam to a relatively high acceleration voltage.
Throughput can also be increased by increasing the maximum beam deflection (i.e., maximum angle with which the beam is laterally deflected) to expose the subfields in each column. By increasing the beam deflection, the length of each column (and thus the width of each stripe) can be increased. I.e., by increasing the width of the stripes, fewer stage movements are required during exposure of the entire reticle pattern. Hence, the cumulative time required to perform stage movements (to expose the subsequent column of subfields or to begin exposing the next stripe of the pattern) during exposure of the reticle pattern is decreased, and throughput is correspondingly increased. Unfortunately, however, a beam experiencing a higher-magnitude deflection must pass through a subfield (located at an end of a column) that is widely separated from the optical axis of the CPB-optical system. Such a high-magnitude deflection generates more deflection aberrations than a lesser-magnitude deflection. The conventional manner of reducing such aberrations is to adjust the excitation current supplied to the deflectors used to deflect the beam and to manipulate the deflection trajectory of the beam so as to minimize deflection aberrations.
Because the magnitude of beam deflection is proportional to the excitation current applied to the deflector, a large excitation current must be impressed on the deflector in order to impart a large-magnitude deflection on the beam. Also, because it is desirable to deflect and scan the beam at high speeds, a driver circuit supplying electrical power to the deflector should be capable of changing the electrical power very rapidly with each subfield. Unfortunately, an electrical circuit capable of performing sufficiently high-speed changes of a high output power is technically difficult and expensive to design. Consequently, there is an urgent need to provide deflectors that can produce as large a deflection as possible using a relatively small electrical current.
The accuracy with which deflectors are manufactured is also crucial for controlling aberrations. Deflectors usually comprise wound coils of an electrical conductor (wire). The conductor itself has a limited thickness, and the accuracy and precision with which most electrical conductors are fabricated are usually not high. As a result, extraneous magnetic fields outside the main deflection field are usually simultaneously generated by the deflector. The distribution of the magnetic field can be expressed using a cylindrical coordinate system (z,r,xcfx86), in which xcfx86 is the rotational angle around the optical axis, r is the radial coordinate and z is the axial coordinate. The reflection field is expressed by the lowest-order trigonometry functions cos[xcfx86], sin[xcfx86], but the magnetic field located outside the deflection field is expressed in terms that are proportional to certain higher odd-ordered trigonometric functions cos[3xcfx86] sin[3xcfx86], cos[5xcfx86], sin[5xcfx86], etc. These higher-order components do not contribute to the deflection of the beam, but do generate group of aberrations referred to as xe2x80x9cfour-fold aberrationsxe2x80x9d (see E. Munro and H. C. Chu, Optik 60:371-390, 1982); and H. C. Chu and E. Munro, Optik 61:121-145, 1982. Because these four-fold a aberrations tend to cause blurring of the image formed by the charged particle beam and undesired changes in the shape of the transfer field, the aberrations are desirably eliminated as much as possible.
Certain deflectors are known in the art that control four-fold aberrations (see Chu and Munro, Optik 61:121-145, 1982, and Orloff (ed.), Handbook of Charged Particle Optics, CRC Press, 1997). However, because the conductors used in deflector coils are thick and deflector fabrication is difficult, it is actually very difficult to produce a deflector with sufficient fabrication accuracy and precision for adequately suppressing four-fold aberrations. Whereas so-called xe2x80x9csaddlexe2x80x9d and xe2x80x9ccompound saddlexe2x80x9d deflectors have the advantages of high deflection sensitivity and relatively low excitation current compared with toroidal deflectors, it is very difficult to fabricate saddle and compound saddle deflectors with high precision accuracy due to the complex shapes of such deflectors.
The present invention addresses the shortcomings of conventional technology summarized above. An object of the invention is to provide charged-particle-beam (CPB) projection-exposure apparatus that can perform large-magnitude deflections of the charged particle beam at low excitation currents and with minimal deflection aberration.
According to one aspect of the invention, CPB exposure apparatus are provided that transfer a pattern, defined on a reticle, onto a sensitive substrate. A first representative embodiment of such an apparatus comprises, inter alia, at least one deflector comprising an xe2x80x9cinner compound saddlexe2x80x9d coil. An inner compound saddle coil has a shape representing a combination of a toroidal coil and a saddle coil. However, a toroidal coil, in contrast to an inner compound saddle coil, has a shape protruding toward the outside of the saddle coil. Hence, the current necessary to impart a particular deflection to the beam using an inner compound saddle coil is substantially reduced (i.e., the deflection sensitivity is correspondingly increased) without compromising blur or distortion compared to a conventional toroidal coil.
In a second representative embodiment, at least one deflector comprises at least two independent deflector coils of different type. Such deflector coils mutually cancel out higher-order components of the magnetic fields generated by the deflector coils. Such canceling out is facilitated by adjusting the respective shape and excitation current of each deflector coil. Consequently, deflection distortion is minimized. By having at least one of the deflector coils being a high-deflection-sensitivity deflector coil, deflection sensitivity is desirably increased overall and larger magnitudes of deflection are desirably obtained at lower excitation currents. The more deflectors having two or more independent deflector coils, the greater the desirable effects obtained. Best results are obtained if all of the deflectors are of such a configuration. The minimum number of deflectors of this configuration is appropriately determined according to the specifications demanded by the CPB exposure apparatus.
In the second representative embodiment, the deflector can comprise an inner compound saddle deflector coil. With such a configuration, the current necessary to achieve a desired deflection is vastly reduced (with a corresponding increase in deflection sensitivity), without compromising blur or distortion compared to a toroidal coil.
Alternatively, the deflector can comprise a combination of a toroidal deflector coil and a saddle deflector coil. The saddle deflector coil is desirably situated coaxially with the toroidal deflector coil at the same position along the optical axis such that the deflectors can be used in combination as a single deflector. With such a configuration, the excitation current required to generate a magnetic field of a desired magnitude can be distributed between the coils and correspondingly reduced, allowing a smaller deflector driver to be used. Since single saddle deflectors and deflectors comprising only saddle deflector coils are difficult to fabricate with high accuracy, such fabrication problems are considerably reduced by combining a saddle coil with a toroidal coil. The respective excitation currents applied to the saddle deflector coil and to the toroidal deflector coil can be fine-tuned. Such tuning achieves an adjustment of the magnetic field generated by the deflector so that magnetic field components proportional to cos[3xcfx86], sin[3xcfx86], cos[5xcfx86], and sin[5xcfx86] (all of which being factors that influence the occurrence of four-fold aberrations) are satisfactorily reduced.
In a deflector comprising a combination of a toroidal deflector coil and a saddle deflector coil, the semi-angle of the saddle deflector coil can be 45xc2x0 or less. By configuring the saddle deflector coil in such a manner, the X-direction deflector and the Y-direction deflector can be situated at the same axial position, which simplifies the manufacture of the deflector and hence of the CPB optical system. Such a configuration also further suppresses four-fold aberrations.
Further with respect to a deflector comprising a combination of a toroidal deflector coil and a saddle deflector coil, the semi-angle of the toroidal deflector coil can be approximately 72xc2x0, and the semi-angle of the saddle deflector coil can be approximately 36xc2x0. With such a configuration, a magnetic field component proportional to cos[5xcfx86] has zero magnitude, which suppresses higher-order aberrations derived from the magnetic field component. In addition, the magnetic field component proportional to cos[3xcfx86] can be reduced to nearly zero magnitude by individually adjusting the excitation currents flowing through these two coils, thereby permitting suppression of higher-order aberrations derived from this component.
The term xe2x80x9capproximatelyxe2x80x9d is used in the context of these semi-angles because, whereas it is ideal that the semi-angles be exactly 72xc2x0 and 36xc2x0, respectively, a certain deviation from the ideal values is allowable. The amount of allowable variation depends on, inter alia, the design precision demanded in the CPB exposure apparatus, and can be readily determined by a person of ordinary skill in the relevant art. In this regard, the terms xe2x80x9capproximatelyxe2x80x9d and xe2x80x9cnearlyxe2x80x9d are used interchangeably herein.
In a deflector comprising a combination of two or more toroidal deflector coils and one saddle deflector coil, the semi-angle of the first toroidal deflector coil is desirably approximately 54xc2x0, the semi-angle of the second toroidal deflector coil is desirably approximately 90xc2x0, and the semi-angle of the saddle deflector coil is desirably approximately 18xc2x0. Such a configuration is effective in suppressing components proportional to cos[3xcfx86] and to cos[5xcfx86]. Indeed, with such a configuration, cos[5xcfx86] components essentially do not appear even if the semi-angle setting for each coil varies from the respective optimal design value of 18xc2x0, 54xc2x0, and 90xc2x0. This is because the integral value of xcfx86 of the magnetic field generated at 5 times the semi-angles of 18xc2x0, 54xc2x0, and 90xc2x0 for each coil, viz., cos[5xcex8], is zero at each of these semi-angles. As a result, the magnetic field is especially stable.
In a deflector comprising a saddle deflector coil and a toroidal deflector coil, the saddle deflector coil can be replaced with a plane-parallel coil residing in a plane not intersecting the optical axis. Such a xe2x80x9cmodifiedxe2x80x9d saddle deflector coil lacks curved surfaces, thereby simplifying the coil profile. Simplifying the coil profile in this manner facilitates high-precision fabrication of the coil and minimizes unexpected aberrations resulting from assembly error.
In a deflector comprising at least one toroidal deflector coil and a compound saddle deflector coil, the semi-angle of the compound saddle deflector coil can be 45xc2x0 or less. For example, the semi-angle of the compound saddle deflector coil can be approximately 36xc2x0, with the semi-angle of the toroidal deflector coil being approximately 72xc2x0. By way of another example, the deflector can comprise two toroidal deflector coils and one saddle deflector coil. In such a configuration, the semi-angle of the first toroidal deflector coil can be approximately 54xc2x0, with the semi-angle of the second toroidal deflector coil being approximately 90xc2x0 and the semi-angle of the compound saddle deflector coil being approximately 18xc2x0. By way of yet another example, the semi-angle of the first toroidal deflector coil can be approximately 69.5xc2x0, the semi-angle of the second toroidal deflector coil can be approximately 90xc2x0, and the semi-angle of the compound saddle deflector coil can be approximately 39xc2x0. In any event, since the cos[3xcfx86] component and the cos[5xcfx86] component are 0 (zero) in these configurations, the respective currents flowing through each coil can be the same. This allows a single coil driver to serve multiple coils, thereby lowering costs.
In a deflector according to the invention, the excitation current supplied to at least one of the deflector coils can be set independently of the excitation currents supplied to the other deflection coils of the deflector. Thus, it is easier for the cos[3xcfx86] component and the cos[5xcfx86] component to be made zero.
The Ampere-Turn value of the respective deflector coils in a deflector according to the invention that comprises a combination of toroidal deflector coils, saddle deflector coils, and/or compound saddle deflector coils can be set so as to fulfill the following Equation (1):                                                         ∑                              i                =                1                            l                        ⁢                          xe2x80x83                        ⁢                                          JT                i                            ·                                                I                  OT3                                ⁡                                  (                                                                                    T                        ⁡                                                  (                          R1                          )                                                                    i                                        ,                                                                  T                        ⁡                                                  (                          R2                          )                                                                    i                                        ,                                                                  T                        ⁡                                                  (                          Zl                          )                                                                    i                                        ,                                          T                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        i                                                                              )                                                              +                                    ∑                              j                =                1                            m                        ⁢                          xe2x80x83                        ⁢                                          JS                j                            ·                                                I                  OS3                                ⁡                                  (                                                            SR                      j                                        ,                                                                  S                        ⁡                                                  (                          Zl                          )                                                                    j                                        ,                                          S                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        j                                                                              )                                                              +                                    ∑                              k                =                1                            n                        ⁢                          xe2x80x83                        ⁢                                          JC                k                            ·                                                I                  OC3                                ⁡                                  (                                                                                    C                        ⁡                                                  (                          R1                          )                                                                    k                                        ,                                                                  C                        ⁡                                                  (                          R2                          )                                                                    k                                        ,                                                                  C                        ⁡                                                  (                          Zl                          )                                                                    k                                        ,                                          C                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        k                                                                              )                                                                    =        0                            (        1        )            
wherein, with respect to the subject deflector, l is the number of toroidal deflector coils; m is the number of saddle deflector coils; n is the number of compound saddle deflector coils; JTi, JSj, and JCk are the Ampere-Turn values of the toroidal deflector coil(s), saddle deflector coil(s), and compound saddle deflector coil(s), respectively; T(R1)i and T(R2)i are the inside radius and outside radius, respectively, of the toroidal deflector coil(s); T(Zl)i is the length along the optical axis of each toroidal deflector coil; Txcex8i is the semi-angle of each toroidal deflector coil; SRi is the radius of each saddle deflector coil; S(Zl)j is the length along the optical axis of each saddle deflector coil; Sxcex8j is the semi-angle of each saddle deflector coil; C(R1)k and C(R2)k are the inside radius and outside radius, respectively, of each compound saddle deflector coil; C(Zl)k is the length along the optical axis of each compound saddle deflector coil; and Cxcex8k is the semi-angle of each compound saddle deflector coil. Also, IOT3(R1,R2,Zlxcex8) is the index function for the toroidal deflector coil, which (where R1 is the inside radius, R2 is the outside radius, Zl is the length along the optical axis, and xcex8 is the semi-angle) is expressed as:                                           I            OT3                    ⁡                      (                          R1              ,              R2              ,              Zl              ,              θ                        )                          =                                            π              NI                        ⁢                                          ∫                                  -                  ∞                                ∞                            ⁢                                                                    Td                    3                                    ⁡                                      (                                          z                      ,                      R1                      ,                      R2                      ,                      Zl                      ,                      θ                                        )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  z                                                              =                                    [                                                2                                      3                    ⁢                                                                  (                        R1                        )                                            3                                                                      -                                  2                                      3                    ⁢                                                                  (                        R2                        )                                            3                                                                                  ]                        ⁢                          xe2x80x83                        ⁢                          (              Zl              )                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            3            ⁢            θ                                              (        2        )            
wherein N is the number of coil windings, I is the excitation current applied to the coil windings, and Td3(z,R1,R2,Zl,xcex8) is defined herein (see Equation (16)). In Equation (2), IOS3(R1,Zl,xcex8) is the index function for the saddle deflector coil, which (where R1 is the radius, Zl is the length along the optical axis, and xcex8 is the semi-angle) is expressed as:                                           I            OS3                    ⁡                      (                          R              ,              Zl              ,              θ                        )                          =                                            π              NI                        ⁢                                          ∫                                  -                  ∞                                ∞                            ⁢                                                                    Sd                    3                                    ⁡                                      (                                          z                      ,                      R                      ,                      Zl                      ,                      θ                                        )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  z                                                              =                                    2              ⁢                              (                Zl                )                            ⁢              sin              ⁢                              xe2x80x83                            ⁢              3              ⁢              θ                                      3              ⁢                              R                3                                                                        (        3        )            
wherein Sd3(z,R,Zl,xcex8) is defined herein (see Equation (17)), and IOC3(R1,R2,Zl,xcex8) is the index function for the compound saddle deflector coil, which is expressed as:                                           I            OC3                    ⁡                      (                          R1              ,              R2              ,              Zl              ,              θ                        )                          =                                                            I                OT3                            ⁡                              (                                  R1                  ,                  R2                  ,                  Zl                  ,                  θ                                )                                      +                                          I                OS3                            ⁡                              (                                  R2                  ,                  Zl                  ,                  θ                                )                                              =                                    2              ⁢                              (                Zl                )                            ⁢              sin              ⁢                              xe2x80x83                            ⁢              3              ⁢              θ                                      3              ⁢                                                (                  R1                  )                                3                                                                        (        4        )            
wherein R1 is the inside radius, R2 is the outside radius, Zl is the length along the optical axis, and xcex8 is the semi-angle.
In Equation (1) the cos[3xcfx86] component is zero. Under such conditions, four-fold aberrations are suppressed by having the Ampere-Turn value in each deflector coil fulfill Equation (1). The more deflectors that satisfy Equation (1), the better. In an optimal configuration, all of the deflectors fulfill Equation (1). However, the skilled person would be able to determine the least number of deflectors that shall fulfill Equation (1), according to the design precision demanded by the CPB exposure apparatus in which the deflector is used.
In at least one deflector other than the deflectors meeting none of the following three conditions, the semi-angle of each respective deflector coil is established such that the Ampere-Turn value for each deflector coil in the deflector is an integer ratio of one another:
(1) a toroidal deflector coil having identical inside radius, outside radius, and length along the optical axis as all of the deflector coils in the deflector;
(2) a saddle deflector coil having identical radius and length along the optical axis in common with all of the deflector coils in a deflector;
(3) a compound saddle deflector coil having identical inside radius, outside radius, and length along the optical axis in common with all of the deflector coils in the deflector.
As noted above, the semi-angle of each deflector coil is determined such that the Ampere-Turn values of the constituent deflector coils are integer ratios (or nearly integer ratios) of each other. As long as the respective numbers of windings in the deflector coils correspond to the respective integers in the ratio, the deflector coils can be driven at the same current, allowing a single coil driver to be used and costs to be reduced.
Similarly, in a deflector having multiple deflector coils including a saddle deflector coil or a modified saddle deflector coil, the radius of the saddle deflector coil, or the distance from the optical axis of the modified saddle deflector coil, can be set such that the respective Ampere-Turn values for the constituent deflector coils are an integer ratio, or nearly an integer ratio, of each other. Further similarly, in a deflector having multiple deflector coils wherein at least one deflector coil is a toroidal deflector coil, the inside radius or outside radius of the toroidal deflector coil can be set such that the Ampere-Turn values of the constituent deflector coils are integer ratios (or nearly integer ratios) of each other. Yet further similarly, in a deflector having multiple deflector coils wherein at least one deflector coil is a compound saddle deflector coil or a modified compound saddle deflector coil, the inside radius or outside radius of the compound saddle deflector coil or modified compound saddle deflector coil can be set such that the Ampere-Turn values of the constituent deflector coils are integer ratios (or nearly integer ratios) of each other.
In at least one deflector, of the deflectors having two or more independent deflector coils, the excitation current applied to each constituent deflector coil can be set to a level that inhibits four-fold aberrations. With such a configuration, a charged particle beam can be obtained that exhibits minimal deflection aberrations. If such a deflector is located downstream of a scattering aperture in the CPB optical system, then the excitation current can be set to a level that inhibits four-fold blur aberration. More specifically, four-fold aberrations are effectively suppressed, by decreasing the cos[3xcfx86] component, with such deflectors located closer to the sensitive substrate than the scattering aperture.
In addition, with such deflectors located downstream of the scattering aperture, the excitation current applied to the deflector can be set to a level that inhibits four-fold coma aberration. More specifically, four-fold coma aberrations are effectively corrected, by decreasing the cos[3xcfx86] component, with such deflectors located closer to the sensitive substrate than the scattering aperture.
In addition, with such deflectors located downstream of the scattering aperture, the excitation current applied to the deflector can be set to a level that inhibits four-fold distortion aberration. As will be explained below, when adjustments are made to suppress four-fold distortion in deflectors closer to the mask plane than the scattering-aperture position, four-fold distortion can be diminished without substantially changing four-fold blur.
The excitation current applied to each deflector coil can be set to a level that inhibits four-fold aberration without substantially changing the deflection sensitivity of the deflector. Since the deflection sensitivity of a deflector is virtually unchanged by the excitation current passed through the various deflector coils to suppress four-fold aberrations, it is unnecessary to perform any new correction to the magnitude of the deflection. The excitation current can be set such that it satisfies (or nearly satisfies) Equation (5), below:                                                         ∑                              i                =                1                            l                        ⁢                          xe2x80x83                        ⁢                                          JT                i                            ·                                                I                  OT1                                ⁡                                  (                                                                                    T                        ⁡                                                  (                          R1                          )                                                                    i                                        ,                                                                  T                        ⁡                                                  (                          R2                          )                                                                    i                                        ,                                                                  T                        ⁡                                                  (                          Zl                          )                                                                    i                                        ,                                          T                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        i                                                                              )                                                              +                                    ∑                              j                =                1                            m                        ⁢                          xe2x80x83                        ⁢                                          JS                j                            ·                                                I                  OS1                                ⁡                                  (                                                            SR                      j                                        ,                                                                  S                        ⁡                                                  (                          Zl                          )                                                                    j                                        ,                                          S                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        j                                                                              )                                                              +                                    ∑                              k                =                1                            n                        ⁢                          xe2x80x83                        ⁢                                          JC                k                            ·                                                I                  OC1                                ⁡                                  (                                                                                    C                        ⁡                                                  (                          R1                          )                                                                    k                                        ,                                                                  C                        ⁡                                                  (                          R2                          )                                                                    k                                        ,                                                                  C                        ⁡                                                  (                          Zl                          )                                                                    k                                        ,                                          C                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        k                                                                              )                                                                    =                  Const          .                                    (        5        )            
wherein, with respect to the deflector, l is the number of toroidal deflector coils; m is the number of saddle deflector coils; n is the number of compound saddle deflector coils; JTi, JSj, and JCk are the Ampere-Turn values of the toroidal deflector coil(s), saddle deflector coil(s), and compound saddle deflector coil(s), respectively; T(R1)i and T(R2)i are the inside radius and outside radius, respectively, of the toroidal deflector coil(s); T(Zl) is the length along the optical axis of each toroidal deflector coil; Txcex8i is the semi-angle of each toroidal deflector coil; SRj is the radius of each saddle deflector coil; S(Zl)j is the length along the optical axis of each saddle deflector coil; SOj is the semi-angle of each saddle deflector coil; C(R1)k and C(R2)k are the inside radius and outside radius, respectively, of each compound saddle deflector coil; C(Zl)k is the length along the optical axis of each compound saddle deflector coil; and Cxcex8k is the semi-angle of each compound saddle deflector coil. In addition, IOT1(R1,R2,Zl,xcex8) is the index function for the toroidal deflector coil (where R1 is the inside radius, R2 is the outside radius, Zl is the length along the optical axis, and xcex8 is the semi-angle) which is expressed as:                                           I            OT1                    ⁡                      (                          R1              ,              R2              ,              Zl              ,              θ                        )                          =                                            π              NI                        ⁢                                          ∫                                  -                  ∞                                ∞                            ⁢                                                                    Td                    1                                    ⁡                                      (                                          z                      ,                      R1                      ,                      R2                      ,                      Zl                      ,                      θ                                        )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  z                                                              =                                    [                                                2                                      (                    R1                    )                                                  -                                  2                                      (                    R2                    )                                                              ]                        ⁢                          (              Zl              )                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            θ                                              (        6        )            
wherein Td1(z,R1,R2,Zl,xcex8) is defined herein (see Equation (13)) and IOS1(R1,Zl,xcex8) is the index function for the saddle deflector coil which is expressed as:                                           I            OS1                    ⁡                      (                          R              ,              Zl              ,              θ                        )                          =                                            π              NI                        ⁢                                          ∫                                  -                  ∞                                ∝                            ⁢                                                                    Sd                    1                                    ⁡                                      (                                          z                      ,                      R                      ,                      Zl                      ,                      θ                                        )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  z                                                              =                                    2              ⁢                              (                Zl                )                            ⁢              sin              ⁢                              xe2x80x83                            ⁢              θ                        R                                              (        7        )            
wherein Sd,(R1,R2,Zl,xcex8) is defined herein (see Equation (13)) and IOC1(R1,R2,Zl,xcex8) is the index function for the compound saddle deflector coil which is expressed as:                                           I            OC1                    ⁡                      (                          R1              ,              R2              ,              Zl              ,              θ                        )                          =                                                            I                OT1                            ⁡                              (                                  R1                  ,                  R2                  ,                  Zl                  ,                  θ                                )                                      +                                          I                OS3                            ⁡                              (                                  R2                  ,                  Zl                  ,                  θ                                )                                              =                                    2              ⁢                              (                Zl                )                            ⁢              sin              ⁢                              xe2x80x83                            ⁢              θ                        R1                                              (        8        )            
wherein IOS3(R2,Zl,xcex8) is defined by Equation (3). Thus, the excitation current for each deflector coil can be set to a level that suppresses four-fold aberrations without changing the deflection sensitivity of the deflector.
In a deflector having two or more independent deflector coils, the excitation current applied to each deflector coil can be set to a level that inhibits four-fold aberration without substantially changing the higher-order aberration of the deflector. With such a configuration, new aberrations are not generated because the higher-order aberrations in the deflector are virtually unchanged, even if the excitation current of each deflector coil is changed to suppress four-fold aberrations. The excitation current is desirably set such that it satisfies (or nearly satisfies) Equation (9), below:                                                         ∑                              i                =                1                            l                        ⁢                          xe2x80x83                        ⁢                                          JT                i                            ·                                                I                  OT5                                ⁡                                  (                                                                                    T                        ⁡                                                  (                          R1                          )                                                                    i                                        ,                                                                  T                        ⁡                                                  (                          R2                          )                                                                    i                                        ,                                                                  T                        ⁡                                                  (                          Zl                          )                                                                    i                                        ,                                          T                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        i                                                                              )                                                              +                                    ∑                              j                =                1                            m                        ⁢                          xe2x80x83                        ⁢                                          JS                j                            ·                                                I                  OS5                                ⁡                                  (                                                            SR                      j                                        ,                                                                  S                        ⁡                                                  (                          Zl                          )                                                                    j                                        ,                                          S                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        j                                                                              )                                                              +                                    ∑                              k                =                1                            n                        ⁢                          xe2x80x83                        ⁢                                          JC                k                            ·                                                I                  OC5                                ⁡                                  (                                                                                    C                        ⁡                                                  (                          R1                          )                                                                    k                                        ,                                                                  C                        ⁡                                                  (                          R2                          )                                                                    k                                        ,                                                                  C                        ⁡                                                  (                          Zl                          )                                                                    k                                        ,                                          C                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        k                                                                              )                                                                    =        0                            (        9        )            
wherein l, m, n, JTi, JSj, JCk, T(R1)i, T(R2)i, T(Zl)i, Txcex8i, SRj, S(Zl)j, Sxcex8j, C(R1)k, C(R2)k, C(Zl)k, and Cxcex8k are defined above. Also, IOT5(R1,R2,Zl,xcex8) is the index function for the toroidal deflector coil which is expressed as:                                           I            OT5                    ⁡                      (                          R1              ,              R2              ,              Zl              ,              θ                        )                          =                                            π              NI                        ⁢                                          ∫                                  -                  ∞                                ∞                            ⁢                                                                    Td                    5                                    ⁡                                      (                                          z                      ,                      R1                      ,                      R2                      ,                      Zl                      ,                      θ                                        )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  z                                                              =                                    [                                                2                                      5                    ⁢                                                                  (                        R1                        )                                            5                                                                      -                                  2                                      5                    ⁢                                                                  (                        R2                        )                                            5                                                                                  ]                        ⁢                          (              Zl              )                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            5            ⁢            θ                                              (        10        )            
wherein Td5(z,R1,R2,Zl,xcex8) is defined herein (see Equation (19)) and IOS5(R1,Zl,xcex8) is the index function for the saddle deflector coil which is expressed as:                                           I            OS5                    ⁡                      (                          R              ,              Zl              ,              θ                        )                          =                                            π              NI                        ⁢                                          ∫                                  -                  ∞                                ∞                            ⁢                                                                    Sd                    5                                    ⁡                                      (                                          z                      ,                      R                      ,                      Zl                      ,                      θ                                        )                                                  ⁢                                  ⅆ                  z                                                              =                                    2              ⁢                              (                Zl                )                            ⁢              sin              ⁢                              xe2x80x83                            ⁢              5              ⁢                              xe2x80x83                            ⁢              θ                                      5              ⁢                              R                5                                                                        (        11        )            
wherein Sd5(z,R,Zl,xcex8) is defined herein (see Equation (20)) and IOC1(R1,R2,Zl,xcex8) is the index function for the compound saddle deflector coil which is expressed as:                                           I            OC5                    ⁡                      (                          R1              ,              R2              ,              Zl              ,              θ                        )                          =                                                            I                OT5                            ⁡                              (                                  R1                  ,                  R2                  ,                  Zl                  ,                  θ                                )                                      +                                          I                OS5                            ⁡                              (                                  R2                  ,                  Zl                  ,                  θ                                )                                              =                                    2              ⁢                              (                Zl                )                            ⁢              sin              ⁢                              xe2x80x83                            ⁢              5              ⁢                              xe2x80x83                            ⁢              θ                                      5              ⁢                                                (                  R1                  )                                5                                                                        (        12        )            
With such a configuration, the excitation current applied to each deflector coil can be set to a level that will suppress four-fold aberrations, virtually without changing the higher-order aberrations in the deflector.